To determine which statement is true, we need to find the y-intercepts of both functions and compare their rates of change.
For Function A: The equation is given as \(y = 8x - 2\). The y-intercept occurs when \(x = 0\): \[ y = 8(0) - 2 = -2 \] So, the y-intercept of Function A is \(-2\).
For Function B: We have the table of values:
- When \(x = -1\), \(y = -2\)
- When \(x = 0\), \(y = -1\)
- When \(x = 1\), \(y = 0\)
- When \(x = 2\), \(y = 1\)
The y-intercept for Function B is also when \(x = 0\): \[ y = -1 \]
Comparison of y-intercepts:
- Function A has a y-intercept of \( -2 \).
- Function B has a y-intercept of \( -1 \).
Thus: \(-2 < -1\), meaning the y-intercept of Function A is less than the y-intercept of Function B.
Rate of Change: The rate of change (slope) of Function A can be determined from its equation \(y = 8x - 2\). The slope is \(8\).
For Function B, we can find the slope using any two points from the table. For example, using points (0, -1) and (1, 0): \[ \text{slope} = \frac{0 - (-1)}{1 - 0} = \frac{1}{1} = 1 \]
Conclusion:
- The y-intercepts are \(-2\) for Function A and \(-1\) for Function B, so the y-intercept of Function A is less than that of Function B.
- The rates of change are \(8\) for Function A and \(1\) for Function B, which are not equal.
Therefore, the correct statement is:
B. The y-intercept of function A is less than the y-intercept of Function B.
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